Originally Posted by

**earboth** Hello,

I'm going to use a coordinate system: Frank's plane starts in (0,0) and Gordon's plane starts in (0, -300). The y-axis is pointing North and the x-axis is pointing **East**. The variable t represents the elapsed time and is measured in hours.

The course of Frank's plane **on the x-axis** is: $\displaystyle f(t)=-650\cdot t$

The course of Gordon's plane **on the y-axis** is: $\displaystyle g(t)=-300+525\cdot t$

The distance between both planes is calculated using the formula for the distance between two points:

$\displaystyle d(t)=\sqrt{(0-(-650\cdot t))^2+(-300+525\cdot t-0)^2}$ = $\displaystyle \sqrt{698125t^2-315000 t+90000}$

The rate of change is d'(t):

$\displaystyle d'(t)=\frac{25(1117 t-252)}{\sqrt{1117t^2-504 t+144}}$

to a) At 9:15 the elapsed time is t=0.25 hours. Plug in this value into d'(t) and you'll get the rate of change: $\displaystyle d'\left(\frac{1}{4}\right)\approx 72,7 \frac{km}{h}$

to b) The approach will cease if the rate of change equals zero:

$\displaystyle d'(t)=0 \text{ if } 1117 t-252=0 \Longleftrightarrow t= \frac{252}{1117}

\approx 13 \text{min}\ 32\text{s}$ when the planes are 233.38 km apart(is that the right expression?)

EB